This paper explores optimizing Integral-Retarded (IR) controller strategies for first-order linear time-delayed processes. By employing a model for DC motor dynamics, we incorporate a design approach that considers an unintentional delay within the control loop. The IR controller is optimized using meta-heuristic algorithms, specifically genetic algorithms. The optimization framework integrates multi-objective cost functions, balancing system response speed and control efforts. Experimental verification is carried out on a physical test setup, where the controller’s efficacy is validated against a square wave reference signal. The outcomes demonstrate that the IR controller, optimized for maximum exponential decay and control efficiency, significantly enhances the motor’s velocity tracking and response smoothness.

This note introduces a geometric approach to devising a modified variant of the conventional Proportional Integral (PI) controller, termed "Proportional Delayed Integral" (PδI). By including an artificial delay in the integral term, we demonstrate that the proposed scheme improves the decay rate attained by the classical PI controller. The analysis involves evaluating the spectral abscissa and employing a geometrical method in both (kp, ki)-plane and (h, ki)-plane. Several numerical examples illustrate the effectiveness of our proposal.

This paper focuses on the characterization of the asymptotic behavior of the critical characteristic roots for a class of delay-differential dynamical systems of neutral type whose coefficients smoothly depend on certain parameters. Such systems can be described by coupled delay-differential and delay-difference equations, and model time heterogeneity in propagation and transport phenomena. The asymptotic behavior of the characteristic roots is addressed by expressing the solutions as a convergent Puiseux series, which facilitates handling multiple solutions. Particular attention is paid to the way the parameters affect the stability of the delay-difference operator. Illustrative examples complete the presentation and show the effectiveness of the proposed method.

This paper presents a new control scheme, named the Proportional Delayed Integral (PδI) controller, for achieving tracking tasks on a tilt-rotor quadrotor. The proposed approach integrates a nonlinear disturbance observer, which effectively mitigates adverse effects stemming from parametric inaccuracies or unknown forces. By enhancing the traditional quadrotor with a tilting mechanism, the operational range is extended, enabling interaction with the surroundings via a robotic arm with one degree of freedom. To ensure precision and adaptability during operations, a comprehensive mathematical model has been meticulously developed, accurately reflecting the unique capabilities of the drone. The synergistic combination of the PδI controller with the nonlinear disturbance observer empowers the tilt-rotor quadrotor to tackle complex tasks with efficiency and reliability. Through rigorous numerical simulations demonstrating the effectiveness of this design, this study lays the foundation for a new era of highly functional and versatile drones, poised to revolutionize various industries and applications.

In this study, we investigate the stabilization of general linear second-order non-minimum phase time-delay systems using PI controllers. Our primary objective is to determine optimal control gains, if any, such that the spectral abscissa of the system is shifted as far left as possible, ensuring enhanced stability. To achieve this, we employ a comprehensive geometrical analysis, providing a methodology to tune the control gains that yield the desired decay rate. The presented approach not only contributes theoretical insights but also facilitates practical implementation. The effectiveness of the proposed methodology is demonstrated through numerical examples.

This paper presents a geometric approach to designing a modified version of the classical PI control called Proportional Delayed Integral (PδI) to obtain the fastest regulation in a type of second-order linear system. Specifically, we first show that by adding an appropriate time delay in the integral component of the PI control, the system achieves a faster response to what can be obtained by using a classical PI control. Then, we outline the conditions under which our delay-based control stabilizes a specific class of second-order systems through an analysis of the spectral abscissa and a graphical approach called D-decomposition. Furthermore, we apply our results to determine the parameters of the fastest regulator.

This work presents a simple procedure for designing fractional PDμcontrollers for a type of implicit operators, which have recently been studied to describe large-scale systems. The methodology developed proposes a geometrical approach that allows characterizing the parameter-space of the PDμcontroller into stable and unstable regions. Several numerical examples illustrate the effectiveness of the proposed results.

The actual paper provides a detailed comparative study of two rotorcraft configurations in terms of their stability with time-delay in the control loop of the system. These configurations correspond to the tilt-rotor (fully-actuated) and fixed-rotor (underactuated) rotorcraft. Such analysis considers the coupling between translation (slow dynamics) and rotational (fast dynamics) motions as a delayed system. Thus, a set of stability charts are presented to illustrate the stability profile for each configuration. We have carried out numerical models that captures essential dynamics of such aerial robots.

The main goal of this paper is to introduce a new non-holonomic model and control of a tilt-rotor aerial robot for interactive operations via a 1DOF robotic manipulator. The modeling is derived by means of the Euler-Lagrange formulation, providing couplings between the robotic manipulator and the rotorcraft. The aerial robot is fully actuated and features thrust vector control, having a more flexible aerial profile. In terms of control, the Immersion and Invariance (I&I) control technique is applied in order to achieve the control objective (trajectory tracking). Finally, preliminary simulation results were conducted to evaluate and validate the control strategy for an interactive tilt-rotor micro aerial vehicle (MAV).

In this paper we present a simple procedure to design fractional-PDμcontrollers for Single-Input-Single-Output-Linear Time Invariant (SISO-LTI) systems with constant time-delay. More precisely, based on a geometric approach, we present a methodology not only to design a stabilizing controller, but also to provide practical guidelines to design non-fragile PDμcontrollers. Finally, in order to illustrate the simplicity of the proposed approach as well as the efficiency of the PDμcontroller in a realistic scenario, we consider an experimental setup consisting of controlling a teleoperated system using two Phantom Omni haptic devices.